TY - GEN
T1 - Analysis in a Formal Predicative Set Theory
AU - Levi, Nissan
AU - Avron, Arnon
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - We present correct and natural development of fundamental analysis in a predicative set theory we call PZFU. This is done by using a delicate and careful choice of those Dedekind cuts that are adopted as real numbers. PZFU is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the sense that every object which is shown in it to exist is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented model of it, and makes it very suitable for MKM (Mathematical Knowledge Management) and ITP (Interactive Theorem Proving). The development of analysis in PZFU does not involve coding, and the definitions it provides for the basic notions (like continuity) are the natural ones, almost the same as one can find in any standard analysis book.
AB - We present correct and natural development of fundamental analysis in a predicative set theory we call PZFU. This is done by using a delicate and careful choice of those Dedekind cuts that are adopted as real numbers. PZFU is based on ancestral logic rather than on first-order logic. Its key feature is that it is definitional in the sense that every object which is shown in it to exist is defined by some closed term of the theory. This allows for a very concrete, computationally-oriented model of it, and makes it very suitable for MKM (Mathematical Knowledge Management) and ITP (Interactive Theorem Proving). The development of analysis in PZFU does not involve coding, and the definitions it provides for the basic notions (like continuity) are the natural ones, almost the same as one can find in any standard analysis book.
KW - Computable set theories
KW - Foundation of mathematics
KW - Predicativity
UR - http://www.scopus.com/inward/record.url?scp=85117452649&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-88853-4_11
DO - 10.1007/978-3-030-88853-4_11
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AN - SCOPUS:85117452649
SN - 9783030888527
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 167
EP - 183
BT - Logic, Language, Information, and Computation - 27th International Workshop, WoLLIC 2021, Proceedings
A2 - Silva, Alexandra
A2 - Wassermann, Renata
A2 - de Queiroz, Ruy
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Workshop on Logic, Language, Information and Computation, WoLLIC 2021
Y2 - 5 October 2021 through 8 October 2021
ER -